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    "###### Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2018 by D. Koehn, notebook style sheet by L.A. Barba, N.C. Clementi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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     "metadata": {},
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   ],
   "source": [
    "# Execute this cell to load the notebook's style sheet, then ignore it\n",
    "from IPython.core.display import HTML\n",
    "css_file = '../style/custom.css'\n",
    "HTML(open(css_file, \"r\").read())"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2D SH finite difference modelling - Love wave propagation in the Fossa Carolina canal\n",
    "\n",
    "After analyzing the accuracy of SH body waves and their free-surface boundary reflections in the previous lessons, we are now able to model SH surface (Love) waves. Instead of using a simplified synthetic sub-surface model, we can rely in this lesson on Full Waveform Inversion (FWI) results of a field dataset acquired across a medieval canal. The reconstructed Vs-model was verified by an archaeological excavation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Fossa Carolina\n",
    "\n",
    "One target of the Priority Program [SPP 1630 ”Harbours from the Roman Periods to the Middle Ages”](http://www.spp-haefen.de/en/home/) by the Deutsche Forschungsgemeinschaft (DFG) is the Fossa Carolina, also known as Charlemagne’s Summit Canal or Karlsgraben in German, in southern Germany. Originally initiated by the Franconian king Charlemagne, as a 3 km long canal to connect the Danube and Rhine river system and thus to overcome the central European watershed, the construction was realized in 793 AD between the rivers\n",
    "Schwäbische Rezat and Altmühl. The Fossa Carolina is one of the most important large-scale hydraulic-engineering projects in the Early Middle Ages. Since 2012 the Fossa Carolina is the aim of interdisciplinary research, covering different areas like archeology, geography and geophysics. Based on a large scale magnetic prospection by the Leibniz-IPHT Jena, more detailed investigations with seismic, ground penetrating radar (GPR), electrical resistivity tomography (ERT) as well as Direct Push measurements have been conducted between 2015 and 2016. Aim of these studies was a more detailed mapping of the canal basement depth to better understand its utilization. Due to the limited penetration depth of the GPR measurements we focused on the results of first arrival traveltime tomography (FATT) and full waveform inversion (FWI) of an SH-dataset acquired along a transect of the Fossa Carolina.\n",
    "\n",
    "The acquisition geometry comprises 47 sources and 48 horizontal component geophones with\n",
    "a receiver spacing of 0.75 m and maximum offsets of 36 m. The acquired data covers a frequency band from 10 Hz to 90 Hz with high signal-to-noise (SN) ratio. Due to the high quality of the field data only a minimum of data pre-processing for the 2D FWI is required. For further details I refer to [Dokter et al. (2017)](https://www.researchgate.net/publication/317336182_Full-waveform_inversion_of_SH-_and_Love-wave_data_in_near-surface_prospecting). In this study we focused on a mono-parameter inversion of the Vs-model, while the Qs and density models are kept fixed. The initial S-wave velocity model is estimated by a FATT, while homogeneous media with Qs = 10 and density ρ = 2000 kg/m 3 are assumed. To reduce the non-linearity of the inverse\n",
    "problem a sequential FWI workflow of low-pass and band-pass filtered data with different bandwidth is applied [(Köhn et al., 2018)](https://www.researchgate.net/publication/324717049_Comparison_of_time-domain_SH_waveform_inversion_strategies_based_on_sequential_low_and_bandpass_filtered_data_for_improved_resolution_in_near-surface_prospecting).\n",
    "\n",
    "In August 2016 the Fossa Carolina canal was excavated along the 2D seismic SH-profile. The derived sketches and photos allow a unique opportunity to directly compare the FWI results with the true structures visible in the subsurface. The photo below taken during the excavation shows a 5.4 m long part of the Fossa Carolina canal between 18.6\n",
    "m and 24.0 m along the 2D SH-profile down to a depth of 1.8 m. \n",
    "\n",
    "<img src=\"images/FATT_FWI_comp_photo_final.jpg\" width=\"100%\">\n",
    "\n",
    "It shows gradual transitions between the layers, except for the very sharp definition of the canal basement. The upper 40 cm of the depth-cut show a weathering layer consisting of soil and vertical cracks. With increasing depth alternating, distinct yellowish and grey clay layers are visible. Near the bottom of the excavation, parts of the black organic-rich layer are uncovered. For a direct comparison of the FWI result, we superimposed image and contour plots of the Vs-models on the excavation photo. The FWI result shows an improved definition of the canal basement by the dense velocity contours, indicating a significant velocity gradient. In contrast to a classical First Arrival Traveltime Tomograpy (FATT), some distinct low- and high velocity anomalies appear within the canal ([Köhn et al., 2018](https://www.researchgate.net/publication/324717049_Comparison_of_time-domain_SH_waveform_inversion_strategies_based_on_sequential_low_and_bandpass_filtered_data_for_improved_resolution_in_near-surface_prospecting), [Köhn et al., 2018a](https://www.researchgate.net/publication/325696342_2D_full_waveform_inversion_applied_to_a_strongly-dispersive_Love_wave_field_dataset_talk)). In some parts, colors of the photo can be directly correlated with the velocity model. For example, the low-velocity contour lines of the FWI Vs-model nearly coincide with the deep yellowish clay layer, the high velocity anomaly above correlates with the grey clay layer. In the weathering layer this correlation is not so clear anymore, because the loose soil and deep-penetrating\n",
    "vertical cracks lead to a reduction of the shear modulus. As a result some dominant near surface low-velocity anomalies down to a depth of 40 cm are introduced.\n",
    "\n",
    "For the derived Fossa Carolina S-wave velocity model, we will now calculate propagation and dispersion of Love waves ... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [
     0
    ]
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   "outputs": [],
   "source": [
    "# Import Libraries \n",
    "# ----------------\n",
    "import numpy as np\n",
    "from numba import jit\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from pylab import rcParams\n",
    "\n",
    "# Ignore Warning Messages\n",
    "# -----------------------\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual, we first define the modelling parameters ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code_folding": [],
    "scrolled": false
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   "source": [
    "# Definition of modelling parameters\n",
    "# ----------------------------------\n",
    "nx = 744  # number of spatial gridpoints in x-direction\n",
    "nz = 120  # number of spatial gridpoints in z-direction\n",
    "\n",
    "dx = 0.05 # spatial gridpoint distance in x-direction\n",
    "dz = dx   # spatial gridpoint distance in z-direction\n",
    "\n",
    "# Define model filename\n",
    "name_vs = \"Fossa_Carolina/Fossa_Carolina_LBL.vs\"\n",
    "\n",
    "tmax = 0.5   # maximum recording time of the seismogram (s)\n",
    "\n",
    "# acquisition geometry\n",
    "xr = 25.5     # x-receiver position (m)\n",
    "zr = 0.05     # z-receiver position (m)\n",
    "\n",
    "xsrc = 17.5   # x-source position (m)\n",
    "zsrc = 0.05    # z-source position (m)\n",
    "\n",
    "f0   = 40. # dominant frequency of the source (Hz)\n",
    "t0   = 4. / f0 # source time shift (s)\n",
    "\n",
    "isnap = 4  # snapshot interval (timesteps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... load the Fossa Carolina S-wave velocity model ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Open file and write binary data to vp\n",
    "f = open(name_vs)\n",
    "data_type = np.dtype ('float32').newbyteorder ('<')\n",
    "vs = np.fromfile (f, dtype=data_type)\n",
    "\n",
    "# Reshape (1 x nx*nz) vector to (nx x nz) matrix \n",
    "vs = vs.reshape(nx,nz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and take a look at the Fossa Carolina model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Fossa Carolina vs-model\n",
    "# ----------------------------\n",
    "\n",
    "# Define xmax, zmax and model extension\n",
    "xmax = nx * dx\n",
    "zmax = nz * dz\n",
    "extent = [0, xmax, zmax, 0]\n",
    "\n",
    "fig = plt.figure(figsize=(15,4))  # define figure size\n",
    "\n",
    "image = plt.imshow((vs.T), cmap=plt.cm.Spectral_r, interpolation='nearest', \n",
    "                   extent=extent, aspect=2)\n",
    "\n",
    "cbar = plt.colorbar(aspect=10, pad=0.02)\n",
    "cbar.set_label('Vs [m/s]', labelpad=10)\n",
    "plt.title('Fossa Carolina model')\n",
    "plt.xlabel('x [m]')\n",
    "plt.ylabel('z [m]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the low velocity layer on top of the model and small scale features within the canal, which could be partly correlated with the archaeological excavation photo. Beside the Vs model, the FD code also requires a density model. Due to the low impact of the density model, we can use a simple homogeneous density model with $\\rho = 1800\\; kg/m^3$ typical for near-surface soil..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho = 1800.0 * (vs / vs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next step, we define the update functions for particle velocity $v_y$ ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Particle velocity vy update\n",
    "# ---------------------------\n",
    "@jit(nopython=True) # use JIT for C-performance\n",
    "def update_vel(vy, syx, syz, dx, dz, dt, nx, nz, rho):\n",
    "    \n",
    "    # 2nd order FD operator   \n",
    "    for i in range(1, nx - 1):\n",
    "        for j in range(1, nz - 1):\n",
    "\n",
    "            # Calculate spatial derivatives  (2nd order operator)           \n",
    "            syx_x = (syx[i,j] - syx[i - 1,j]) / dx\n",
    "            syz_z = (syz[i,j] - syz[i,j - 1]) / dz\n",
    "\n",
    "            # Update particle velocities\n",
    "            vy[i,j] = vy[i,j] + (dt/rho[i,j]) * (syx_x + syz_z)                               \n",
    "                \n",
    "    return vy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... updating the shear stress components $\\sigma_{yx}$ and $\\sigma_{yz}$ ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Shear stress syx, syz updates\n",
    "# -----------------------------\n",
    "@jit(nopython=True) # use JIT for C-performance\n",
    "def update_stress(vy, syx, syz, dx, dz, dt, nx, nz, mux, muz):\n",
    "    \n",
    "    # 2nd order FD operator\n",
    "    for i in range(1, nx - 1):\n",
    "        for j in range(1, nz - 1):\n",
    "\n",
    "            # Calculate spatial derivatives (2nd order operator)\n",
    "            vy_x = (vy[i + 1,j] - vy[i,j]) / dx\n",
    "            vy_z = (vy[i,j + 1] - vy[i,j]) / dz\n",
    "\n",
    "            # Update shear stresses\n",
    "            syx[i,j] = syx[i,j] + dt * mux[i,j] * vy_x\n",
    "            syz[i,j] = syz[i,j] + dt * muz[i,j] * vy_z                    \n",
    "    \n",
    "    return syx, syz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and harmonically averaging the shear modulus ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Harmonic averages of shear modulus\n",
    "# ----------------------------------\n",
    "@jit(nopython=True) # use JIT for C-performance\n",
    "def shear_avg(mu, nx, nz, mux, muz):\n",
    "    \n",
    "    for i in range(1, nx - 1):\n",
    "        for j in range(1, nz - 1):\n",
    "            \n",
    "            # Calculate harmonic averages of shear moduli        \n",
    "            mux[i,j] = 2 / (1 / mu[i + 1,j] + 1 / mu[i,j])\n",
    "            muz[i,j] = 2 / (1 / mu[i,j + 1] + 1 / mu[i,j])\n",
    "            \n",
    "    return mux, muz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To avoid boundary reflections from the bottom as well as left and right boundary, we use the simple Sponge boundary frame, which was introduced for the 2D acoustic code in [this lesson](http://nbviewer.jupyter.org/github/daniel-koehn/Theory-of-seismic-waves-II/blob/master/05_2D_acoustic_FD_modelling/4_fdac2d_absorbing_boundary.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define simple absorbing boundary frame based on wavefield damping \n",
    "# according to Cerjan et al., 1985, Geophysics, 50, 705-708\n",
    "def absorb(nx,nz):\n",
    "\n",
    "    FW = 60     # thickness of absorbing frame (gridpoints)    \n",
    "    a = 0.0053\n",
    "    \n",
    "    coeff = np.zeros(FW)\n",
    "    \n",
    "    # define coefficients in absorbing frame\n",
    "    for i in range(FW):    \n",
    "        coeff[i] = np.exp(-(a**2 * (FW-i)**2))\n",
    "\n",
    "    # initialize array of absorbing coefficients\n",
    "    absorb_coeff = np.ones((nx,nz))\n",
    "\n",
    "    # compute coefficients for left grid boundaries (x-direction)\n",
    "    zb=0 \n",
    "    for i in range(FW):\n",
    "        ze = nz - i - 1\n",
    "        for j in range(zb,ze):\n",
    "            absorb_coeff[i,j] = coeff[i]\n",
    "\n",
    "    # compute coefficients for right grid boundaries (x-direction)        \n",
    "    zb=0\n",
    "    for i in range(FW):\n",
    "        ii = nx - i - 1\n",
    "        ze = nz - i - 1\n",
    "        for j in range(zb,ze):\n",
    "            absorb_coeff[ii,j] = coeff[i]\n",
    "\n",
    "    # compute coefficients for bottom grid boundaries (z-direction)        \n",
    "    xb=0 \n",
    "    for j in range(FW):\n",
    "        jj = nz - j - 1\n",
    "        xb = j\n",
    "        xe = nx - j\n",
    "        for i in range(xb,xe):\n",
    "            absorb_coeff[i,jj] = coeff[j]\n",
    "\n",
    "    return absorb_coeff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we assemble all parts into the 2D SH FD code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "code_folding": [
     42
    ]
   },
   "outputs": [],
   "source": [
    "# 2D SH Wave Propagation (Finite Difference Solution) \n",
    "# ---------------------------------------------------\n",
    "def FD_2D_SH_JIT(dt,dx,dz,f0,xsrc,zsrc,vs,rho):        \n",
    "            \n",
    "    nt = (int)(tmax/dt) # maximum number of time steps            \n",
    "    print('nt = ',nt)\n",
    "    \n",
    "    ir = (int)(xr/dx)      # receiver location in grid in x-direction    \n",
    "    jr = (int)(zr/dz)      # receiver location in grid in z-direction\n",
    "\n",
    "    # Source time function (Gaussian)\n",
    "    # -------------------------------\n",
    "    src  = np.zeros(nt + 1)\n",
    "    time = np.linspace(0 * dt, nt * dt, nt)\n",
    "\n",
    "    # 1st derivative of a Gaussian\n",
    "    src  = -2. * (time - t0) * (f0 ** 2) * (np.exp(- (f0 ** 2) * (time - t0) ** 2))\n",
    "\n",
    "    # define wavefield clip value    \n",
    "    clip = 1e-5\n",
    "    \n",
    "    # Initialize coordinates\n",
    "    # ----------------------\n",
    "    x    = np.arange(nx)\n",
    "    x    = x * dx       # coordinates in x-direction (m)\n",
    "\n",
    "    z    = np.arange(nz)\n",
    "    z    = z * dz       # coordinates in z-direction (m)\n",
    "    \n",
    "    # calculate 2D Green's function for direct SH wave from source position    \n",
    "    isrc = (int)(xsrc/dx)  # source location in grid in x-direction\n",
    "    jsrc = (int)(zsrc/dz)  # source location in grid in x-direction            \n",
    "    \n",
    "    # Initialize empty pressure arrays\n",
    "    # --------------------------------\n",
    "    vy    = np.zeros((nx,nz)) # particle velocity vy\n",
    "    syx   = np.zeros((nx,nz)) # shear stress syx\n",
    "    syz   = np.zeros((nx,nz)) # shear stress syz        \n",
    "    \n",
    "    # define shear modulus\n",
    "    # --------------------\n",
    "    mu = rho * vs**2\n",
    "    \n",
    "    # harmonic average of shear moduli\n",
    "    # --------------------------------\n",
    "    mux   = mu # initialize harmonic average mux \n",
    "    muz   = mu # initialize harmonic average muz\n",
    "\n",
    "    mux, muz = shear_avg(mu, nx, nz, mux, muz)\n",
    "    \n",
    "    # Initialize empty seismogram\n",
    "    # ---------------------------\n",
    "    seis = np.zeros(nt) \n",
    "    \n",
    "    # Define absorbing boundary frame\n",
    "    # -------------------------------    \n",
    "    absorb_coeff = absorb(nx,nz)\n",
    "    \n",
    "    # Initalize animation of vy wavefield \n",
    "    # -----------------------------------\n",
    "    fig = plt.figure(figsize=(7,3))  # define figure size\n",
    "    extent = [0.0,xmax,zmax,0.0]     # define model extension\n",
    "    \n",
    "    # Plot Vp-model\n",
    "    image = plt.imshow((vs.T), cmap=plt.cm.gray, interpolation='nearest', \n",
    "                        extent=extent, aspect=2)    \n",
    "    \n",
    "    # Plot vy wavefield movie\n",
    "    image1 = plt.imshow(vy.T, animated=True, cmap=\"RdBu\", alpha=.75, extent=extent, \n",
    "                          interpolation='nearest', aspect=2, vmin=-clip, vmax=clip)\n",
    "    \n",
    "    plt.title('Vy wavefield')\n",
    "    plt.xlabel('x [m]')\n",
    "    plt.ylabel('z [m]')\n",
    "           \n",
    "    plt.ion()    \n",
    "    plt.show(block=False)\n",
    "    \n",
    "    # Time looping\n",
    "    # ------------\n",
    "    for it in range(nt):\n",
    "    \n",
    "        # Update particle velocity vy\n",
    "        # ---------------------------\n",
    "        vy = update_vel(vy, syx, syz, dx, dz, dt, nx, nz, rho)\n",
    "\n",
    "        # Add Source Term at (isrc,jsrc)\n",
    "        # ------------------------------\n",
    "        # Absolute particle velocity w.r.t analytical solution\n",
    "        vy[isrc,jsrc] = vy[isrc,jsrc] + (dt * src[it] / (rho[isrc,jsrc] * dx * dz))\n",
    "        \n",
    "        # Apply absorbing boundary frame to vy\n",
    "        # ------------------------------------\n",
    "        vy *= absorb_coeff        \n",
    "        \n",
    "        # Update shear stress syx, syz\n",
    "        # ----------------------------\n",
    "        syx, syz = update_stress(vy, syx, syz, dx, dz, dt, nx, nz, mux, muz)                \n",
    "        \n",
    "        # Apply absorbing boundary frame to syx, syz\n",
    "        # ------------------------------------------\n",
    "        syx *= absorb_coeff\n",
    "        syz *= absorb_coeff\n",
    "        \n",
    "        # Output of Seismogram\n",
    "        # -----------------\n",
    "        seis[it] = vy[ir,jr]\n",
    "        \n",
    "        # display vy snapshots \n",
    "        if (it % isnap) == 0:            \n",
    "            image1.set_data(vy.T)\n",
    "            fig.canvas.draw()\n",
    "        \n",
    "    return time, seis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with the modelling of the wave propagation and seismogram for a homogeneous model with the average S-wave velocity of the Fossa Carolina model and constant density $\\rho = 1800\\; kg/m^3$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nt =  3369\n"
     ]
    },
    {
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       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"\" width=\"699.9999721845002\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run SH FD modelling for homogeneous model\n",
    "# -----------------------------------------\n",
    "%matplotlib notebook\n",
    "\n",
    "# define homogeneous model\n",
    "vs0 = np.mean(vs) * (vs / vs)\n",
    "rho0 = 1800.0 * (vs / vs)\n",
    "\n",
    "# calculate time step according to CFL criterion\n",
    "dt = dx / (np.sqrt(2) * np.max(vs0)) \n",
    "\n",
    "time, seis_hom = FD_2D_SH_JIT(dt,dx,dz,f0,xsrc,zsrc,vs0,rho0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"\" width=\"699.9999721845002\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot FD Seismogram\n",
    "# ------------------\n",
    "%matplotlib notebook\n",
    "# Define figure size\n",
    "rcParams['figure.figsize'] = 7, 5\n",
    "plt.plot(time, seis_hom, 'b-',lw=3,label=\"FD solution\") # plot FD seismogram\n",
    "plt.xlim(time[0], time[-1])\n",
    "plt.title('Seismogram (homogeneous model)')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though the model contains a free surface, no Love wave propagates in the homogeneous model. We only see the direct SH body wave. One way to understand the origin and propagation of Love waves is by the interference of SH body waves in a layered medium, which explains why no Love waves propagate in a homogeneous medium. A mathematically more detailed description of the problem was given in the \"Theory of Seismic Waves\" lecture [(Müller 2007)](http://gfzpublic.gfz-potsdam.de/pubman/item/escidoc:8728:5/component/escidoc:8727/0703.pdf).\n",
    "\n",
    "So let's turn to the heterogeneous Fossa Carolina canal model, where the seismic wavefield should be dominated by Love waves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nt =  6487\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"\" width=\"699.9999721845002\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run SH FD modelling for heterogeneous Fossa Carolina canal model\n",
    "%matplotlib notebook\n",
    "# calculate time step according to CFL criterion\n",
    "dt = dx / (np.sqrt(2) * np.max(vs)) \n",
    "\n",
    "time, seis_fossa = FD_2D_SH_JIT(dt,dx,dz,f0,xsrc,zsrc,vs,rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"\" width=\"699.9999721845002\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot FD Seismogram\n",
    "# ------------------\n",
    "%matplotlib notebook\n",
    "# Define figure size\n",
    "rcParams['figure.figsize'] = 7, 5\n",
    "plt.plot(time, seis_fossa, 'b-',lw=3,label=\"FD solution\") # plot FD seismogram\n",
    "plt.xlim(time[0], time[-1])\n",
    "plt.title('Seismogram (Fossa Carolina model)')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, a quite impressive, dispersive Love wave sticking to the free-surface on top of the model, penetrating down to a depth of 3 m for the low-frequency part, while the high frequency Love waves propagate in the upper 1 m. Notice also the amplitude differences in the seismograms for the direct SH body wave (6e-6 m/s) in the homogeneous model and the Love wave (6e-5 m/s) in the heterogeneous Fossa Carolina canal.\n",
    "\n",
    "##### Excercise\n",
    "\n",
    "You might wonder why we used such a simple homogeneous density model despite the heterogeneous sub-surface. To investigate the impact of a realistic heterogeneous density model on the Love-wavefield, compute a heterogeneous density model for the Fossa Carolina canal based on the Vs-model with an empirical density $\\rho$ - S-wave velocity model $V_s$ relation from [Ulugergerli & Uyanık (2007)](https://www.researchgate.net/publication/249958795_Statistical_Correlations_Between_Seismic_Wave_Velocities_and_SPT_Blow_Counts_and_the_Relative_Density_of_Soils):\n",
    "\n",
    "\\begin{equation}\n",
    "\\rho = 0.1055\\; ln(V_s)\\; +\\; 1.3871\\notag\n",
    "\\end{equation}\n",
    "\n",
    "with the units for $V_s$ $[m/s]$ and density $\\rho$ $[g/cm^3]$. Compute the Love-/SH-wavefield for the Fossa Carolina canal model with the heterogeneous density model and compare the resulting seismograms with the previous result for the homogeneous density model. Discuss differences and similarities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What we learned:\n",
    "\n",
    "* Implementation of the simple Sponge boundary for the 2D SH-problem\n",
    "* Love waves do not propagate in a homogeneous SH medium\n",
    "* Dispersive Love waves propagte in the heterogeneous Fossa Carolina canal model, where the penetration depth is frequency dependent"
   ]
  }
 ],
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